# Full text of "Analytical Mechanics"

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```MOTION                                     75
pare and identify different bodies by means of these properties. In selecting one of these properties to represent the body in our study of motion we must see that the property fulfills two conditions: that it is intimately related to motion and that it is constant.
Weight is often used to represent a body in its motion. So far as bodies on the earth are concerned weight is intimately connected with motion, but it is not constant. Besides, when bodies are far from the earth, weight does not have a definite meaning. Therefore weight does not satisfy the foregoing conditions. The property which serves the purpose best is known as mass. It is intimately connected with motion and is constant.* The nature of this property will be discussed in the next chapter. - Therefore we will content ourselves by defining mass as that property with which bodies are represented in discussions of their motion.
73.   Unit of Mass.—-The unit of mass is the gram, which is voVo" Par* °^ ^e mass of the standard kilogram.   The latter is the mass of a piece of platinum in the possession of the French Government.
74.   Dimensions.—-The fundamental magnitudes enter into the composition of one derived magnitude in a manner different from the way they enter into that of a second.   Length alone enters into the composition of an area, while velocity contains both length and time, and all three of the fundamental magnitudes combine in work and momentum.    The expression which gives the manner in which time, length, and mass combine to form a derived magnitude is called the dimensional formula of that magnitude.    Thus the dimensional formulae for area, velocity, and momentum are, respectively,
[A] = [L2],    [7] = [LIT1],  and  [H] = [MLT^l
where M, L, and T represent length, mass, and time. The exponent of each letter is called the dimension of the de-
* Cf. §101.```